1. Field of the Invention
The present invention is directed to a chromatic diffractive optical element (DOE) corrector. More particularly, the present invention is directed to a DOE corrector formed on two surfaces for use with multiple wavelengths.
2. Description of Related Art
Numerous applications require a single objective lens to be used for multiple wavelengths. In many such cases, there are three wavelengths for which the lens is to be used. For example, in blue laser based digital video disc (DVD) systems, it is desirable that these systems remain backwards compatible with red laser DVD systems and compact disc (CD) systems, which use infrared (IR) lasers. Each different color may require different focal lengths and/or different numerical apertures.
One conventional solution includes using one surface having a first phase function providing a high first order efficiency for red and a second phase function providing a high first order efficiency for IR, while providing high zeroth order efficiency for blue. In order to achieve this, a thick DOE needs to be used. For example, to make phase levels that are multiples of 2π for the blue wavelength, the phase delay for a transmission DOE is given by:2π(n−1)d/λ  (1)where n is the index of refraction of the DOE for blue light, d is the thickness of the DOE and lambda is the wavelength of the blue light. The 2π thickness D for each wavelength and corresponding refractive index is given by:D=λ/(n−1)  (2)
Thus, for example, if a DOE is designed to transmit 407 nm (blue light), impart the first phase function on 650 nm (red light) and impart the second phase function on 785 nm (IR), since 785 nm is nearly twice 407 nm, levels which effect 785 nm but would not effect 407 nm need to be determined. The phase levels would be determined from integer multiples M of D that do not effect the blue light. For most materials this results in very thick elements with relatively low efficiency, especially in the IR, e.g., less than 50%.
In this current solution using one surface to diffract two of the three wavelengths, phase levels for a first phase function at a first wavelength, e.g., 650 nm, are selected that correspond to a zero phase delay (modulo 2π) or about zero phase delay for the other two wavelengths, e.g., 407 nm and 785 nm. For a second phase function at a second wavelength, e.g., 785 nm, phase levels are chosen to correspond to zero for the other two wavelengths, e.g., 407 nm and 650 nm. Assume the phase levels are provided in a material having no dispersion and a refractive index of 1.46. For simplification, consider only solutions MD for blue light. In designing the second phase function and restricting the multiple of D to M≦40, and then looking for values of M within this range where the phase angle for the red light is less than ±20°, then there are five values for M which satisfy this condition. However, these phase levels also need to provide phase angles close to 0°, 90°, 180° and 270° for a four phase level diffractive for the IR light. Only three of the five values are within ±20° of these target values. A diffractive other than a binary diffractive would thus need to be made with more than a thickness of M=40 at 407 nm, i.e., more than 35 microns thick.
The actual is problem is even more severe than in this simplified case, since the refractive index of fused silica actually decreases as wavelength increases, i.e., positive dispersion. Thus, the refractive index of fused silica is actually 1.470 at 405 nm, 1.457 at 650 nm, and 1.453 (at 785 nm). This dispersion results in the blue and IR light becoming even more closely harmonic, as can be seen with reference to the following phase delay ratio of Equation (3):
                                          λ            B                                (                                          n                B                            -              1                        )                                                λ            IR                                (                                          n                IR                            -              1                        )                                              (        3        )            Without dispersion, i.e., when nB=nIR, this phase delay ratio is 1.93, while in fused silica, it becomes 2.01. With these refractive indices, when M is selected to be an integer for the blue light, then phase values for the IR light will all be within ±10° of either 0° or 180° for all values of M<75, resulting in a DOE having a thickness of at least 65 microns to realize even a four level DOE.
Thus, when using fused silica, the conventional approach is limited to a binary DOE for IR light, unless a very thick diffractive structure, e.g., much thicker than 65 microns, is used. Such a binary DOE has very low efficiency, roughly 40%, compared with roughly 80% for a four-level DOE. Thicker DOEs are a problem, as they are more difficult to fabricate, and generally don't perform as well due to shadowing. Shadowing is due to the relative aspect ratios of the etch depth and the period. For manufacturability, this aspect ratio should be less than about two, and the etch depth should less than about 35 microns. Materials other than fused silica, such as plastic, have been used, as these materials have a larger dispersion than for fused silica, allowing the phase delay ratio to exceed 2.0 and move further from the harmonic. However, in these higher dispersion materials, the proper operation of the first phase function for the red light becomes a problem, especially while achieving proper operation of the second phase function.